Convexity invariants like Caratheodory, Helly and Radon numbers are computed for triangle path convexity in graphs. Unlike minimal path convexities, the Helly and Radon numbers behave almost uniformly for triangle path convexity. c © 1999 Elsevier Science B.V. All rights reserved

In this paper continuing our work started in [Br1]-[Br3] we prove the corona theorem for the algebra of bounded holomorphic functions defined on an unbranched covering of a Caratheodory hyperbolic Riemann surface of finite type.

This paper characterizes the asymptotic convergence properties of the primal-dual dynamics to the solutions of a constrained concave optimization problem using classical notions from stability analysis. We motivate our study by providing an example which rules out the possibility of employing the invariance principle for hybrid automata to analyze the asymptotic convergence. We understand the s...

This paper studies the asymptotic convergence properties of the primal-dual dynamics designed for solving constrained concave optimization problems using classical notions from stability analysis. We motivate the need for this study by providing an example that rules out the possibility of employing the invariance principle for hybrid automata to study asymptotic convergence. We understand the ...

Models of social influence may present discontinuous dynamical rules, which are unavoidable with topological interactions, i.e. when the dynamics is outcome interactions a limited number nearest neighbors. Here, we show that classical solutions not sufficient to describe resulting dynamics. We first time evolution interaction graph associated Caratheodory solutions, whose properties depend on d...

Let M be a C∞ Riemannian manifold, dimM = n. A distribution on M is a smooth linear subbundle of the tangent bundle TM . We denote by q the fiber of at q ∈M ; q ⊂ TqM . The number k = dim q is the rank of the distribution. We assume that 1 < k < n. The restriction of the Riemannian structure to is a sub-Riemannian structure. Lipschitz integral curves of the distribution are called admissible pa...